Quaternions for regularizing Celestial Mechanics: the right way

Details Quaternions for regularizing Celestial Mechanics: the right way Quaternions for regularizing Celestial Mechanics: the right way

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cemda.102..149w&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 102, Issue 1-3, pp. 149-162

Astronomy and Astrophysics

Astronomy

4

Quaternions, Regularization, Kustaanheimo&Ndash, Stiefel Transformation, Kepler Formulas, Birkhoff Transformation, Perturbed Kepler Problem, Joukowsky-Birkhoff Mapping, Quaternion Algebra

Scientific paper

Quaternions have been found to be the ideal tool for describing and developing the theory of spatial regularization in Celestial Mechanics. This article corroborates the above statement. Beginning with a summary of quaternion algebra, we will describe the regularization procedure and its consequences in an elegant way. Also, an alternative derivation of the theory of Kepler motion based on regularization will be given. Furthermore, we will consider the regularization of the spatial restricted three-body problem, i.e. the spatial generalization of the Birkhoff transformation. Finally, the perturbed Kepler motion will be described in terms of regularized variables.

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